Pressure-Induced Structural Transformation in Cristobalite Studied by Molecular Dynamic Simulations
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ABSTRACT The phase transformation between the a- and 13-cristobalite modifications of SiO2 were studied using molecular dynamic simulations. The transformation was induced isothermally by control of the pressure within the structure, either through an externally applied constant stress or by changing the simulation box volume. The atomic scale mechanisms of the transformation can best be observed by means of a time-correlation function describing the spatial orientation of the planes containing the Si-O-Si bonds. These planes rotate by 90" over the course of the transition. Both, the bulk modulus, calculated for static structures, as well as the vibrational spectra of the Si-O-Si planes, reflect the softening of acoustic modes in the midst of the transition, which is characteristic of displacive phase transformations. Although the aperiodic shift of atomic positions upon passage of the transformation front could be responsible for a momentary softening of the structure, this is not the only reason, since this behavior persists when maintaining the structure at intermediate densities, which corresponds neither to a-, nor to Ilcristobalite. INTRODUCTION The high temperature phase of silica SiO2, the fl-cristobalite polymorph, is stable between 1470"C and the melting point 1728°C. Using a rapid cooling, this phase persists metastably down to about 275°C and is then transformed to the low temperature phase cz-cristobalite. The f'a strong hysteresis effect.(1 ) a phase transition is first order; it is rapid and reversible, but2 1shows 0 However, in spite of a long history of investigations.( - ) this phase transition remains controversial because the interpretation of experimental findings is not unequivocal. Molecular dynamic simulations are quite powerful in complementing such an analysis, they provide a detailed view of atomic structures and their motion. In a previous because study( 11) we demonstrated this by simulating the infra-red response of various silica structures, including a- and fP-cristobalite, and by identifying the strict correspondence between spectral bands, structural feature and its vibrational modes. It was then that we discovered the ease and reliability with which phase transition occurred in the simulated model. In the present paper, we provide a more detailed analysis of the mechanisms involved in the a to P3phase transition in cristobalite. COMPUTATIONAL PROCEDURE The molecular dynamic simulation method and the model for atomic interactions, which includes ionic and covalent contributions, have previously been described in detail.0 1) Longrange Coulomb interactions were treated by means of an Ewald summation, and covalent interactions were modeled using a three-body term and partial charge transfer. The simulations involved bulk specimens, which require the assumption of periodic boundary conditions. The time increment between re-evaluation of energy and forces was 2.10-15 s. All the simulations corresponding to discussed here involved 648 particles (216 Si and 432 0) with initial positions t
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